Mordred

Here is one of the better papers for the graviton spin 2. Note equation [math]g_{\mu\nu}\rightarrow \eta_{\mu\nu}+k h_{\mu\nu}[/math] https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/gr-qc/0607045&ved=2ahUKEwjCzqGC1PXmAhW1oFsKHT-HAs4QFjAAegQIBBAB&usg=AOvVaw30-hmokcbjp_amGXWvZtet The article provides the general spin Compton scattering for the other spin statistics as well as spin 2. My recommendation is to start with the linearized Einstein Hilbert action. See the following Doctorate thesis. (It's a common methodology for modelling the graviton) https://www.google.com/url?sa=t&source=web&rct=j&url=https://academiccommons.columbia.edu/download/fedora_content/download/ac:201929/content/GarciaSaenz_columbia_0054D_13501.pdf&ved=2ahUKEwi90_f23vXmAhX6JTQIHd0cCU8QFjACegQIAhAB&usg=AOvVaw22sjBJZaLwriZmm2fuX0wt By using the Einstein Hilbert action your already working in quanta Ie quanta of action and thus can make the correlations to the creation and annihilation operators for the Feymann path integrals. Though the difficulty will be avoiding infinite one loop corrections. Divergence that ruins renormalization Edit almost forgot in the above equation [math]k^2=16\pi G [/math] I'm not sure any of the above articles mention that. The above formula is a fairly standard equation in numerous papers for massless spin 2 propogators.

Much better for the Jacobian in spherical weak field limit. However It looks to me your graviton application is spin 1 dipolar. You need quaternion relations spin 2 (quadrupolar). To match up to gravity wave data. ( Though I will have to study your equations for reference 6 further) Let dig up some good graviton modelling and the relevant GR spin 2 application. Keep in mind in order to properly model the gravitons you will need it's wavefunction for transerve and longitudinal component. (In gauge treatments you must be renormalizable. )

Lol I always seem to get caught by spell check lol. Correction made thanks for the catch

Here is one example Schwartzchild metric Vacuum solution [latex]T_{ab}=0[/latex] which corresponds to an unaccelerated freefall frame [latex]G_{ab}=dx^adx^b[/latex] if [latex]ds^2> 0[/latex] =spacelike propertime= [latex]\sqrt{ds^2}[/latex] [latex]ds^2<0[/latex] timelike =[latex]\sqrt{-ds^2}[/latex] [latex] ds^2=0[/latex] null=lightcone spherical polar coordinates [latex](x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)[/latex] [latex] G_{\alpha\beta} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}[/latex] line element [latex]ds^2=-(1-\frac{2M}{r}dt)^2+(1-\frac{2M}{r})^{-1}+dr^2+r^2(d \phi^2 sin^2\phi d\theta^2)[/latex]

Lol correction applied

[math]g_{\alpha\beta}[/math] is the metric tensor the indices run (0,1,2,3). The form will vary according to the spacetime being modelled it can have either or both the covariant and contravariant terms accordingly to the Einstein summation convention. In the above its specifying covariant.

[math]\mu\cdot\nu=\nu\cdot\mu=\eta [/math] is the inner product symmetry relations for the Minkowskii metric tensor. You identified it as the GR symmetry matrix expression. You need the first order partials for the Jacobian matrix while I don't have polar coordinate form handy you can look here for the Minkowskii form though you will have to switch the signature. https://en.m.wikipedia.org/wiki/Four-gradient The one forms mentioned are invariant under coordinate change

Lol considering I am only 5 foot seven and 155 lbs my legs can press 250 kg for ten reps on a Universal machine. 60 kg is nothing.

You would deal with the position and momentum uncertainty with quantum particles however relativity itself is a classical theory which it's mathematics doesn't incorporate probabilities or harmonic oscillators for the uncertainty principle. Those get incorporated when you deal with theories such as QFT. However freefall paths via principle of least action (Langrangian) does involve uncertainty in the chosen path that the particle will take at each infinisimal. (GR itself doesn't get too much into the Langrangian) so when studying GR I wouldn't worry about uncertainty in freefall paths. That's would be far too distracting until you get really comfortable with GR

Welcome back and excellent post as always. I particularly agree with your caveat that spacetime is a mathematical model.

Higgs field with above [math]\mathcal{L}=(D_\mu H)^\dagger D^\mu H-\lambda(H^\dagger H-\frac{v^2}{2})^2[/math] v=246 GeV Quartic coupling [math]\lambda=m_h^2/2v^2=0.13[/math] [math]\langle H^\dagger H\rangle =v^2/2[/math] Fermions (matter content) (goal tie in CKMS and Pmns mixing angles (latter for leptons)) will require unity triangle... [math]\displaystyle{\not}D=\gamma D^\mu[/math] self reminder Feymann slash contraction of the gamma matrix with a four vector [math]\displaystyle{\not}a=\gamma a^\mu a_\nu=\gamma_\mu a^\nu[/math] a is any four vector.

Pulling this post back to where I can find it to add Yukawa couplings details this weekend [math]\mathcal{G}=SU(3)_c\otimes SU(2)_L\otimes U(1)_Y[/math] Color, weak isospin, abelion Hypercharge groups. Couplings in sequence [math]g_s, g, \acute{g}[/math] [math]\mathcal{L}_{gauge}=-\frac{1}{2}Tr{G^{\mu\nu}G_{\mu\nu}}-\frac{1}{2}Tr {W^{\mu\nu}W_{\mu\nu}}-\frac{1}{4}B^{\mu\nu}B_{\mu\nu}[/math] Field strengths in sequence in last G W B tensors for SU(3),SU(2) and U(1) Leads to covariant derivative [math]D_\mu=\partial_\mu+ig_s\frac{\lambda_i}{2}G^i_\mu+ig\frac{\sigma_i}{2}W^i_\mu+igQ_YB_\mu[/math] Corresponds to [math]G_{\mu\nu}=-\frac{i}{g_s}[D_\mu,D_\nu][/math] [math]W_-\frac{I}{g}[D_{\mu}D_{\nu}][/math] [math]B_{\mu\nu}-\frac{I}{\acute{g}}[D_\mu,D_\nu][/math]

[math]\acute{D1}=\frac{D1 c}{(c-V)}[/math] do you think this statement is correct ? Sorry but this just doesn't make any sense. Why didn't you just use Galilean relativity to start with ? [math]\acute{x}=x-vt [/math] [math]\acute{t}=t [/math] [math]\acute{y}=y [/math] [math]\acute{z}=z [/math]

From what I can tell he is rambling. Particularly since he also stated Ie no seperation distance ???? Tell me OP when are you ever going to address direct questions correctly ? Every response you give leads to more confusion. Sounds like you don't know how to describe your theory. Your now invoking virtual phase and group velocity but still haven't shown how your keeping the phase velocity equal to c for all observers... This asked of you by several posters.... Now here is another question for you you specifically stated a wave requires a medium to propogate. So why does both you phase and group velocities have wave equations ? Perhaps you should start with the basics [math]v=\lambda f [/math] [math]k=\frac{2\pi}{\lambda}[/math] [math]f=\frac{2\pi}{\omega}[/math] At least you can start with the basic electromagnetic wave equations. You should at least realize in a vacuum you can have any frequency or wavelength as long as [math]\lambda f=c [/math] Though if you want the modern method use https://en.m.wikipedia.org/wiki/Electromagnetic_wave_equation Though you would have to admit your phase and group velocity usage is completely wrong in modern terminology usage.

I have read your papers and the biggest lack I can see is that you haven't understood that physicists in the early years do not understand basic wave mechanics. You are quite wrong on that aspect. Please define absolute motion including the vector transformation rules required to keep phase velocity equal to c for all observers. Unless you can do that I don't see any validity in your theory. pS mathematics not words. From what I have read your theory requires you definition of phase velocity being equal to c for all observers. So provide the necessary vector transformation rules required under 3d treatment to produce that requirement.

One of the problems ppl have when they present ether based theories is the assumption that the tests have stopped at the more commonly known tests. There have been dozens of different tests looking for an ether that all show null results the latest that I am familiar with was done in 2009. This test looked for Ether at the quantum level with its extreme precision. [math]\Delta c/c=1*10^{-17}[/math] for the precision level. Still absolutely no indication of an ether. @Op your going to need some incredibly strong evidence well beyond any mathematics your papers indicate to account for how these null results can occur with your theory. Quite frankly without extremely accurate precision tests you really don't have much hope in competing with the overwhelming evidence against you. Here is the relevent arxiv to the result above https://arxiv.org/abs/1002.1284

Well I for one have no confidence of validity from what I have read thus far. Too many inaccuracies in the paper in terms of what is involved in stated experiments. Good example being the M$M experiment where the frame dragging aspect of an absolute frame is ignored as one example. From what I can determine non standard use of the terms phase and group velocities. Though quite frankly having an absolute frame using wavefuctions makes absolutely zero sense under vector symmetry treatments. Particularly one being emitted from a moving source. You would still require time dilation and length contraction to keep the phase velocity constant.

I realize that Studiot but quite frankly I am unclear if he truly understands the difference between a phase velocity and a group velocity. So I gave an example. Relativity also does little to define a particle as per wavefunction states. Yet this is important to understand why relativity doesn't deal with phase velocity but the group velocity. Ie an earlier statement the phase velocity does not describe the particle velocity the group velocity does. This relates back to the following question if you think about it. If the OP sets the phase velocity as constant and equal to c then the group velocity must equal the phase velocity to satisfy the equation you posted. In the case of a massive particles who's group velocity is less than c the phase velocity must exceed c. You must apply both the massless and massive case under relativity but the OP clearly doesn't understand why the group velocity is the particle velocity.

Phase velocity varies depending on its wavelength in a dispersive medium. The only time it can be constant is in a vacuum. However group velocity is also constant in a vacuum. If you have a paper showing otherwise please post it (preferably arxiv) I'll bet there is some medium involved in those papers. In essence in circumstances where w does not equal ck. However your still missing one key problem. [math] the group velocity and not the phase velocity describes the velocity of a particle [/b] Good example the QM or QFT superposition particle state is described via its group velocity.

I too look forward to seeing how the OP is defining group and phase velocity as none of his descriptives match the mainstream definitions.

I would also suspect an absolute frame would have additional ramifications for GW waves. Even in gravitational lensing there is no indication of a refractive index you would distortions that are not present on observation. Not to mention CMB distortions or lack of.

You obviously didn't read or understand a single formula I posted if your still declaring this to be a problem. In a vacuum the group and phase velocity are both constant. A vacuum isn't a dispersive medium. Perhaps you need to understand that first. As mainstream science already does. Not that phase velocity has anything to do with particle velocity. Which is also important to understand. It is the group velocity that is important to redshift. Redshift isn't due to dispersion. If it was it would have some funky side effects on spectronomy measurements of the hydrogen 21 cm line

When In a vacuum the following electromagnetic relations for phase and group vecocities [math]\omega=ck [/math] [math]v=\frac{\omega}{k}=\frac{\partial\omega}{\partial k}=c[/math] The group velocity will equal the phase velocity both will equal c to all observers. The constant c is frequency independant. See dispersion relations given here https://en.m.wikipedia.org/wiki/Dispersion_relation

Unfortunately the OP isn't using any of the correct formulas to properly correlate phase velocity or group velocity in terms of the energy momentum equation. The phase velocity is not the velocity of the particle the group velocity is. https://en.m.wikipedia.org/wiki/Matter_wave Group velocity (equal to the particle's speed) should not be confused with phase velocity (equal to the product of the particle's frequency and its wavelength). In the case of a non-dispersive medium, they happen to be equal, but otherwise they are not. you can read further on that link but if you ever do the calculations you will find that for any particle less than c the phase velocity will always exceed c. However that is a product of its frequency and wavelength as noted by that link. It does not represent the velocity of the particle even in the case of photons. edit one side note phase velocity is not a true velocity but an apparent velocity it will not allow superluminal communication even if it's value exceeds c. You are dealing with group velocities in redshift equations whatever of the three primary types and not the phase velocity for the reasons above. Primary reason is the phase velocity carries no energy. Which is why it doesn't violate causality. (In a vacuum the phase velocity and the group velocity of light is equal) particularly since a vacuum is NOT a dispersive medium with a refractive index. Phase velocity has nothing to do with your claims above in point of detail a dispersive medium is precisely when the phase velocities become distinctive from the group group velocities. (As different wavelengths respond differently with the refractive index) primary example a prism.

It's more accurate to not think of evolution as being caused by some factor. Rather the adaptations that best suit an environment is the more successful. There are also unsuccessful adaptations that do not suit an environment those get weeded out by survival of the fittest. The problem is thinking innovation can cause evolution, or the advantages an evolutionary change as being a cause regardless of what that advantage is. In essence evolution is the result of successful adaptations or mutations. No advantage gained by bipedalism causes the evolutionary change the advantages are the result of the successful changes.